DD-RNO: A Domain-Decomposed Routed Neural Operator for Airfoil Flow Prediction

Abstract

Deep learning surrogates for RANS flow prediction around airfoils face two persistent bottlenecks. A single neural architecture cannot simultaneously resolve sharp near-wall boundary layers and smooth far-field potential flow. Additionally, force prediction is undermined by the numerical instability of computing wall-normal velocity gradients from continuous-field approximations. Both of these points are addressed with a DD-RNO (domain-decomposed routed neural operator), combining a spectral geometry encoder with two physics-guided innovations: (a) a differentiable domain routing mechanism that partitions the flow field into inviscid, boundary-layer, and wake regimes---dispatching query points to specialized regional decoders, and (b) learned canonical quadrature (LCQ), which replaces unstable pressure integration with flow-conditioned, learned integration weights that predict lift and drag directly from surface pressure. On the AirfRANS benchmark, DD-RNO cuts velocity field mean-square error (MSE) by 17$x$ ($u_x$) and 12$x$ ($u_y$) over the strongest baseline, widening to 23$x$ under out-of-distribution Reynolds extrapolation---evidence that the routing mechanism generalizes with the physics it encodes rather than merely fitting the training distribution. LCQ reduces drag MSE by 7.5$x$ relative to conventional pressure integration and raises drag rank correlation from $ρ= 0.250$ to $ρ= 0.997$. Ablations confirm that both components are indispensable to performance: removing domain routing increases velocity error by 8.2$x$, and removing LCQ increases relative drag error more than 40-fold. At ~144 ms per sample---a 10,000$x$ speedup over conventional RANS solvers---DD-RNO offers a surrogate accurate and fast enough for real-time aerodynamic design and optimization loops.